Simulation of dielectric resonator for high-Tc radio frequency superconducting quantum interference device

Nowadays, the high-critical-temperature radio frequency superconducting quantum interference device (high-$T_{\rm c }$ rf SQUID) is usually coupled to a dielectric resonator that is a standard $10\times 10\times 1$~mm³ SrTiO$₃ (STO) substrate with a YBa₂Cu$₃O$_{7 - \delta }$ (YBCO) thin-film flux focuser deposited on it. Recently, we have simulated a dielectric resonator for the high-$T_{\rm c }$ rf SQUID by using the ANSOFT High Frequency Structure Simulator (ANSOFT HFSS). We simulate the resonant frequency and the quality factor of our dielectric resonator when it is unloaded or matches a 50-$\Omega$ impedance. The simulation results are quite close to the practical measurements. Our study shows that ANSOFT HFSS is quite suitable for simulating the dielectric resonator used for the high-$T_c rf SQUID. Therefore, we think the ANSOFT HFSS can be very helpful for investigating the characteristics of dielectric resonators for high-$T_c rf SQUIDs.